I will show that the basic argument which you have used in assuming that Adi Shankara's many stotrams are incorrectly attributed to him is erroneous.
First of all a saint,rishi or an acharya don't compose stotrams only for their benefit.
The basic idea is that those who will read them in future will be benefited.This thing becomes evident from the phalasrutis of various stotrams as well.
From phalasruti of Adi Shankara's Kanakadhara Stotram :
Those who glorify with this Hymn, everyday, ...
18.2: ... the Ramaa (Devi Lakshmi) Who is Trayimayi (The embodiment of the Three Vedas) and Mother of the Three Worlds, ...
18.3: ... will be filled with abundant Virtues, and be blessed with the destiny of very Venerable persons,
18.4: They will become Wise in the World by Your Grace awakening their Wisdom.
So,its evident that here Shankara is composing the stotram for all those who are stricken with poverty.
Similarly, from the phalasruti of Sri Vyasa Krutha Bhagavati Stotram :
6.1: This Stotram (Hymn) is Composed by Sage Vyasa,
6.2: Whoever Recites this Stotram Regularly after becoming Bodily and Mentally Clean ,...
6.3: ...in his Home or Anywhere with Pure Devotion to the Goddess,
6.4: Will Please the Bhagavati Devi Always.
So,this is the real motive behind composing stotrams.Mahamunis like Vyasa don't compose stotrams for themselves but for the benefits of common people like me.Similar is the case with Adi Shankara.
In the Subhramanya Bhujangam Adi Shankara says:
2.1: (Salutations to Sri Subramanya) I know neither Words, nor their Meanings O Lord,
2.2: And I know neither Poetry, nor Prose, but
So,are we to take this literally ?
Even in Bhavani Ashtakam(another composition of Adi Shankara) we find the following verses:
Bhavaabdhaav-Apaare Mahaa-Duhkha-Bhiiru Papaata Prakaamii Pralobhii
Pramattah | Ku-Samsaara-Paasha-Prabaddhah Sada-[A]ham Gatis-Tvam
Gatis-Tvam Tvam-Ekaa Bhavaani ||2||
2.1: In this Ocean of Worldly Existence which is Endless, I am full of Sorrow and Very much Afraid,
2.2: I have Fallen with Excessive Desires and Greed, Drunken and Intoxicated,
2.3: Always Tied in the Bondage of this miserable Samsara (worldly existence),
2.4: You are my Refuge, You Alone are my Refuge, Oh Mother Bhavani.
Na Jaanaami Daanam Na Ca Dhyaana-Yogam Na Jaanaami Tantram Na Ca
Stotra-Mantram | Na Jaanaami Puujaam Na Ca Nyaasa-Yogam Gatis-Tvam
Gatis-Tvam Tvam-Ekaa Bhavaani ||3||
3.1: Neither do I know Charity, nor Meditation and Yoga,
3.2: Neither do I know the practice of Tantra, nor Hymns and Prayers,
3.3: Neither do I know Worship, nor dedication to Yoga,
3.4: You are my Refuge, You Alone are my Refuge, Oh Mother Bhavani.
5.1: I performed Bad Deeds, associated with Bad Company, cherished Bad Thoughts, have been a Bad Servant,
5.2: I did not perform my Traditional Duties, deeply engaged in Bad Conducts,
5.3: My eyes Saw with Bad Intentions, tongue always Spoke Bad Words,
5.4: You are my Refuge, You Alone are my Refuge, Oh Mother Bhavani.
अनाथो दरिद्रो जरारोगयुक्तो महाक्षीणदीनः सदा जाड्यवक्त्रः । विपत्तौ
प्रविष्टः प्रनष्टः सदाहं गतिस्त्वं गतिस्त्वं त्वमेका भवानि ॥८॥
Anaatho Daridro Jaraa-Roga-Yukto Mahaa-Kssiinna-Diinah Sadaa
Jaaddya-Vaktrah | Vipattau Pravissttah Pranassttah Sadaaham Gatis-Tvam
Gatis-Tvam Tvam-Ekaa Bhavaani ||8|
8.1: I am Helpless, Poor, Afflicted by Old Age and Disease,
8.2: Very Weak and Miserable, always with a Pale Countenance,
8.3: Fallen Asunder, Always surrounded by and Lost in Troubles and Miseries,
8.4: You are my Refuge, You Alone are my Refuge, Oh Mother Bhavani.
Its obvious that Adi Shankara is talking on behalf of all those people who may have committed sins and now seeking surrender in Divine Mother and not for himself.So,even if he is talking about age in some stotrams, we should interpret it like the way i have.
As the final reference i am using Durga Stava Raja(the king of all prayers to Durga) also known as Durga Apaduddhakraka Stotram composed by Lord Shiva himself.This stotram is found in many Agama texts like Rudra Yamala,Viswa Sara Tantram and in Sri Siddheswari Tantram.
Take this verse from the stotram;
अरण्ये रणे दारुणे शुत्रुमध्ये जले सङ्कटे राजग्रेहे प्रवाते । त्वमेका
गतिर्देवि निस्तार हेतुर्नमस्ते जगत्तारिणि त्राहि दुर्गे ॥ ४॥
You are the only refuge and the boat that saves, Me from the forest,
war, danger and from midst of enemies, Me from fire, ocean, from enemy
territory and from forts of kings, And so salutations to you who saves
the universe, With a request,”Please protect me oh, Durga”.
So,are we to take this literally as if Lord Shiva is asking for himself all these?Obviously not.Here Lord Shiva is asking on behalf of those who are inflicted with those dangers and who will be reading the stotram in times of such Apadas(dangers).